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C25×AGL(1,𝔽23) #27162500

order12650
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C2×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C11×C25)
unambiguous semidirect product(C23⋊C11)⋊(C2×C25)
unambiguous semidirect product(C25×D23)⋊C11

Splittings

Fitting, HallC23×C25 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C11×C25
HallC25×C23⋊C11 ⋊ C2
HallC25×D23 ⋊ C11
HallC23⋊C11 ⋊ C2×C25
HallD23 ⋊ C11×C25

Subgroups

subgroupG/H
center, hypercenterC25AGL(1,𝔽23)
commutator, hypocenterC23C2×C11×C25
FrattiniC5C5×AGL(1,𝔽23)
FittingC23×C25C2×C11
socle, cosocleC5×C23C2×C5×C11
prime radicalC5×AGL(1,𝔽23)C5
LCSG ▷ C23
UCSC1 ◁ C25

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 575

A minimal faithful permutation representation — 2 generators on 48 points:

(2,5,6,13,14,21,16,17,7,18,19,3,4,8,9,20,15,10,22,11,12,23)(24,25,27,30,34,26,28,31,35,39,29,32,36,40,43,33,37,41,44,46,38,42,45,47,48);(1,2,4,7,6,10,12,20,9,15,17,23,19,22,21,13,14,18,16,8,11,5,3)

Conjugacy classes & character table

575 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD25×AGL(1,𝔽23), C2×C25×AGL(1,𝔽23), C3×C25×AGL(1,𝔽23), …
maximal normal subgroup ofD25×AGL(1,𝔽23), C2×C25×AGL(1,𝔽23), C3×C25×AGL(1,𝔽23)
maximal quotient ofC25×Dic23⋊C11, C2×C25×AGL(1,𝔽23), C3×C25×AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12650, 11);