Finite Group Databasebeta

C2×#11926378 #14565927

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

Aliases

direct productC2×#11926378

Splittings

SylowC19 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D19
commutatorC2×C19C22×C16
FrattiniC16C22×D19
FittingC22×C16×C19C2
socleC22×C19C2×C16
prime radicalC23×C19C16
cosocleC16×C19C23
hypercenterC22×C16D19
hypocenterC19C2×M64
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C16 ◁ C22×C16

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#18070227, #18070228, #18070229, …
maximal normal subgroup of#18070227, #18070228, #18070229, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6802);