Finite Group Databasebeta

C2×#11926377 #14565926

order2432
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11926377

Splittings

FittingC2×C19×C32 ⋊ C2
SylowC19 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D19
commutatorC2×C19C22×C16
FrattiniC16C22×D19
FittingC2×C19×C32C2
socleC22×C19C2×C16
prime radicalC22×D19C16
cosocleC16×C19C23
hypercenterC2×C32D19
hypocenterC19C2×M64
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C16 ◁ C2×C32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18070349
maximal normal subgroup of#18070349

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6801);