Finite Group Databasebeta

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#496×Dic43 #25105140

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct product#496×Dic43

Splittings

SylowC43 ⋊ C4×#496

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#496C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#496D43
hypocenterC43C4×#496
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

1262 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 178111);