Finite Group Databasebeta

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C8×#13063284 #25094800

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#13063284

Splittings

SylowC43 ⋊ C8×#117

Subgroups

subgroupG/H
centerC2×C4×C8C2×D43
commutatorC2×C43C22×C4×C8
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C8×#117
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

1174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167771);