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ΓL(1,𝔽8)×Dic131 #24926994

order11004
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×Dic131
unambiguous semidirect productC131⋊(C4×ΓL(1,𝔽8))
unambiguous semidirect product(C7×Dic131)⋊C3

Splittings

derived, HallC7×C131 ⋊ C3×C4
HallC7×Dic131 ⋊ C3
HallΓL(1,𝔽8)×C131 ⋊ C4
SylowC131 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×Dic131

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D131
commutator, hypocenterC7×C131C3×C4
Fitting, socle, cosocleC2×C7×C131C2×C3
prime radicalC2×ΓL(1,𝔽8)×C131C2
LCSG ▷ C7×C131
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

670 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×ΓL(1,𝔽8)×Dic131, ΓL(1,𝔽8)×Dic393
maximal normal subgroup ofC3×ΓL(1,𝔽8)×Dic131
maximal quotient ofC7⋊C9×Dic131, C3×ΓL(1,𝔽8)×Dic131, ΓL(1,𝔽8)×Dic393

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11004, 10);