Finite Group Databasebeta

C2×Dic304 #14565940

order2432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic304

Splittings

SylowC19 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D304
commutator, cosocleC16×C19C23
FrattiniC16C22×D19
FittingC2×C19×C32C2
socle, prime radicalC22×C19D16
hypercenterC2×C32D19
hypocenterC19C2×Q64
LCSG ▷ C16×C19 ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18070419, #18070421, #18070431, …
maximal normal subgroup of#18070419, #18070421, #18070431, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6815);