Finite Group Databasebeta

← Prev (#23750689) Next (#23750691) →

C2×Q8×#10597010 #23750690

order9536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#10597010
unambiguous semidirect productD149⋊(C4×Q8)

Splittings

FittingC2×Q8×C149 ⋊ C4
SylowC149 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#10597010
commutatorC2×C149C23×C4
FrattiniC2C23×#10597010
FittingC2×Q8×C149C4
socleC22×C149C22×C4
prime radicalC22×D149C23
cosocleC2×D149C24
hypercenterC2×Q8#10597010
hypocenterC149C2×C4×Q8
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

410 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#101×#10597010, #103×#10597010, #34060464, …
maximal normal subgroup of#101×#10597010, #103×#10597010, #34060464, …
maximal quotient ofC2×C4⋊C4×#10597010, C4×Q8×#10597010, C2×#23750574, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 1614);