Finite Group Databasebeta

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C22×#14582620 #25062165

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×#14582620

Splittings

SylowC43 ⋊ C22×#322

Subgroups

subgroupG/H
centerC22×C42C2×D43
commutatorC2×C43C22×C4×C8
FrattiniC42C23×D43
FittingC22×C4×C8×C43C2
socle, prime radicalC24×C43C42
cosocleC42×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C22×#322
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1182 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, 135136);