Finite Group Databasebeta

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C2×Q8×#10624382 #26042344

order11584
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#10624382
unambiguous semidirect productD181⋊(C4×Q8)

Splittings

FittingC2×Q8×C181 ⋊ C4
SylowC181 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#10624382
commutatorC2×C181C23×C4
FrattiniC2C23×#10624382
FittingC2×Q8×C181C4
socleC22×C181C22×C4
prime radicalC22×D181C23
cosocleC2×D181C24
hypercenterC2×Q8#10624382
hypocenterC181C2×C4×Q8
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

490 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#101×#10624382, #103×#10624382, #37549494, …
maximal normal subgroup of#101×#10624382, #103×#10624382, #37549494, …
maximal quotient ofC2×C4⋊C4×#10624382, C4×Q8×#10624382, C2×#26042228, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1614);