Finite Group Databasebeta

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C2×Q8×#10621924 #26012556

order11072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#10621924
unambiguous semidirect productD173⋊(C4×Q8)

Splittings

FittingC2×Q8×C173 ⋊ C4
SylowC173 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#10621924
commutatorC2×C173C23×C4
FrattiniC2C23×#10621924
FittingC2×Q8×C173C4
socleC22×C173C22×C4
prime radicalC22×D173C23
cosocleC2×D173C24
hypercenterC2×Q8#10621924
hypocenterC173C2×C4×Q8
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

470 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#101×#10621924, #103×#10621924, #36369336, …
maximal normal subgroup of#101×#10621924, #103×#10621924, #36369336, …
maximal quotient ofC2×C4⋊C4×#10621924, C4×Q8×#10621924, C2×#26012440, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 1614);