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C101×C3⋊(ΓL(1,𝔽8)⋊C4) #38764151

order25452
automorphism?
homologyAbelianization (H1) = C3×C4×C101 · Schur multiplier (H2) = C1

Aliases

direct productC101×C3⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)⋊C4×C101)
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic3×C101)
unambiguous semidirect productDic21⋊(C3×C101)
unambiguous semidirect product(Dic21×C101)⋊C3

Splittings

derivedC3×C7 ⋊ C3×C4×C101
HallC3×ΓL(1,𝔽8)×C101 ⋊ C4
HallC7×C101 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C101
SylowC7 ⋊ C3×Dic3×C101

Subgroups

subgroupG/H
center, hypercenterC2×C101C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C3×C4×C101
FrattiniC2C101×C3⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C101C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C101C2
cosocleC2×C3×C7C2×C3×C101
LCSG ▷ C3×C7
UCSC1 ◁ C2×C101

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8484

Conjugacy classes & character table

2424 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25452, 45);