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ΓL(1,𝔽8)×Dic97 #22550899

order8148
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×Dic97

Splittings

derived, HallC7×C97 ⋊ C3×C4
HallC7×Dic97 ⋊ C3
HallΓL(1,𝔽8)×C97 ⋊ C4
SylowC97 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×Dic97

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D97
commutator, hypocenterC7×C97C3×C4
Fitting, socleC2×C7×C97C2×C3
LCSG ▷ C7×C97
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

500 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×Dic97⋊C3, C3×ΓL(1,𝔽8)×Dic97, ΓL(1,𝔽8)×Dic291
maximal normal subgroup ofΓL(1,𝔽8)×Dic97⋊C3, C3×ΓL(1,𝔽8)×Dic97
maximal quotient ofC7⋊C9×Dic97, C3×ΓL(1,𝔽8)×Dic97, ΓL(1,𝔽8)×Dic291

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8148, 14);