Finite Group Databasebeta

C4×#10597392 #14566164

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#10597392

Splittings

FittingC2×C4×Q8×C19 ⋊ C2
SylowC19 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC2×C4×Q8×C19C2
socle, cosocleC23×C19C24
prime radicalC23×D19C23
hypercenterC2×C4×Q8D19
hypocenterC19C4×C22⋊Q8
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

656 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#18077057, #18077062, #18077077, …
maximal normal subgroup of#18077057, #18077062, #18077077, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7039);