Finite Group Databasebeta

C2×Dic1192 #23750053

order9536
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic1192

Splittings

SylowC149 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D1192
commutator, cosocleC8×C149C23
FrattiniC8C22×D149
FittingC2×C16×C149C2
socle, prime radicalC22×C149D8
hypercenterC2×C16D149
hypocenterC149C2×Q32
LCSG ▷ C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2390 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34042871, #34042873, #34042883, …
maximal normal subgroup of#34042871, #34042873, #34042883, …
maximal quotient ofC2×#23749430, C2×#23749451, C4×Dic1192, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 977);