Finite Group Databasebeta

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C4×#14582675 #25011419

order11008
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct productC4×#14582675

Splittings

SylowC43 ⋊ C4×#346

Subgroups

subgroupG/H
centerC2×C4×C8C2×D43
commutatorC2×C43C42×C8
FrattiniC22×C8C22×D43
FittingC42×C8×C43C2
socle, prime radicalC23×C43C22×C8
cosocleC22×C8×C43C23
hypercenterC42×C8D43
hypocenterC43C4×#346
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4×C8 ◁ C42×C8

510 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, 84390);