Finite Group Databasebeta

← Prev (#14523521) Next (#14523523) →

C25×ΓL(1,𝔽8)⋊C4 #14523522

order2100
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C25)
unambiguous semidirect productDic7⋊(C3×C25)
unambiguous semidirect product(C25×Dic7)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C25
HallC25×Dic7 ⋊ C3
HallΓL(1,𝔽8)×C25 ⋊ C4
HallC7×C25 ⋊ C3×C4
HallDic7 ⋊ C3×C25
HallΓL(1,𝔽8) ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C25
FrattiniC2×C5C5×AGL(1,𝔽7)
FittingC2×C7×C25C2×C3
socle, cosocleC2×C5×C7C2×C3×C5
prime radicalC2×C5×ΓL(1,𝔽8)C2×C5
LCSG ▷ C7
UCSC1 ◁ C2×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 700

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(27,31,30,28,29,32)(33,34,35,36);(26,27,30,31,29,32,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC25×(C49⋊C3)⋊C4, C7×C25×ΓL(1,𝔽8)⋊C4, C25×#10596874, …
maximal normal subgroup ofC7×C25×ΓL(1,𝔽8)⋊C4, C11×C25×ΓL(1,𝔽8)⋊C4, C13×C25×ΓL(1,𝔽8)⋊C4, …
maximal quotient ofC25×(C49⋊C3)⋊C4, C7×C25×ΓL(1,𝔽8)⋊C4, C25×#10596874, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 2);