Finite Group Databasebeta

C22×#10597275 #14572210

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#10597275

Splittings

SylowC19 ⋊ C22×#107

Subgroups

subgroupG/H
centerC24D76
commutatorC4×C19C23×C4
FrattiniC2×C4C23×D19
FittingC23×C8×C19C2
socle, prime radicalC24×C19D4
cosocleC2×C4×C19C24
hypercenterC23×C8D19
hypocenterC19C22×#107
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18088437, #18088439, #18088441, …
maximal normal subgroup of#18088437, #18088439, #18088441, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 13085);