Finite Group Databasebeta

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Q8×#13063243 #25113169

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#13063243

Splittings

SylowC43 ⋊ Q8×#101

Subgroups

subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutator, prime radicalC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingQ8×M16×C43C2
socleC22×C43C22×C22⋊C4
cosocleC22×C4×C43C24
hypercenterQ8×M16D43
hypocenterC43Q8×#101
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

970 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 186140);