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ΓL(1,𝔽8)×Dic103 #22575741

order8652
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×Dic103

Splittings

derived, HallC7×C103 ⋊ C3×C4
HallC7×Dic103 ⋊ C3
HallΓL(1,𝔽8)×C103 ⋊ C4
SylowC103 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×Dic103

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D103
commutator, hypocenterC7×C103C3×C4
Fitting, socleC2×C7×C103C2×C3
LCSG ▷ C7×C103
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

530 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×(C103⋊C3)⋊C4, C3×ΓL(1,𝔽8)×Dic103, ΓL(1,𝔽8)×Dic309
maximal normal subgroup ofΓL(1,𝔽8)×(C103⋊C3)⋊C4, C3×ΓL(1,𝔽8)×Dic103
maximal quotient ofC7⋊C9×Dic103, C3×ΓL(1,𝔽8)×Dic103, ΓL(1,𝔽8)×Dic309

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8652, 14);