Finite Group Databasebeta

C2×Dic184 #13092845

order1472
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic184

Splittings

SylowC23 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D184
commutator, cosocleC8×C23C23
FrattiniC8C22×D23
FittingC2×C16×C23C2
socle, prime radicalC22×C23D8
hypercenterC2×C16D23
hypocenterC23C2×Q32
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

Relationships

maximal subgroup of#15671577, #15671579, #15671589, …
maximal normal subgroup of#15671577, #15671579, #15671589, …
maximal quotient ofC2×#13092222, C2×#13092243, C4×Dic184, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1472, 977);