Finite Group Databasebeta

C2×#11927098 #14576923

order2432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#11927098

Splittings

FittingC2×C4×Q8×C19 ⋊ C2
SylowC19 ⋊ C2×#533

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC2×C4×Q8×C19C2
socleC23×C19C24
prime radicalC23×D19C23
hypercenterC2×C4×Q8D19
hypocenterC19C2×#533
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

1168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18073921
maximal normal subgroup of#18073921

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17798);