Finite Group Databasebeta

C2×#11927251 #14577166

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

Aliases

direct productC2×#11927251

Splittings

SylowC19 ⋊ C2×#554

Subgroups

subgroupG/H
centerC23C23×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC2×C4×D4×C19C2
socleC23×C19C24
prime radicalC22×D4×C19C22
hypercenterC2×C4×D4D19
hypocenterC19C2×#554
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C4×D4

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18074225, #18074228, #18074300, …
maximal normal subgroup of#18074225, #18074228, #18074300, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 18041);