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C3×AGL(1,𝔽5)×C23 #13063407

order1380
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C23

Splittings

Fitting, socle, HallC3×C5×C23 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C23
HallC5×C23 ⋊ C3×C4
HallC3×C5 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC3×C23AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C23
FrattiniC1G
Fitting, socleC3×C5×C23C4
prime radicalC3×D5×C23C2
cosocleD5C2×C3×C23
LCSG ▷ C5
UCSC1 ◁ C3×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 345

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3)(5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(4,5,6,8,7)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×AGL(1,𝔽5)×C23, C32×AGL(1,𝔽5)×C23, C3×C23×ΓL(1,𝔽16), …
maximal normal subgroup ofC9×AGL(1,𝔽5)×C23, C32×AGL(1,𝔽5)×C23, C3×AGL(1,𝔽5)×C23⋊C11, …
maximal quotient ofC9×AGL(1,𝔽5)×C23, C32×AGL(1,𝔽5)×C23, C3×C23×ΓL(1,𝔽16), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1380, 10);