Finite Group Databasebeta

C2×#11926307 #14563349

order2432
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11926307

Splittings

SylowC19 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24D76
commutatorC4×C19C2×C42
FrattiniC22×C4C22×D19
FittingC23×C8×C19C2
socle, prime radicalC24×C19D4
cosocleC22×C4×C19C23
hypercenterC23×C8D19
hypocenterC19C2×#340
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

512 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#18069682, #18069684, #18069700, …
maximal normal subgroup of#18069682, #18069684, #18069700, …
maximal quotient ofC2×#14561470, #18072005, #18072015, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 4224);