Finite Group Databasebeta

C2×#21422355 #28510378

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21422355

Splittings

SylowC59 ⋊ C2×#1442

Subgroups

subgroupG/H
centerC25C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC23×C4⋊C4×C59C2
socle, prime radicalC25×C59C23
cosocleC24×C59C24
hypercenterC23×C4⋊C4D59
hypocenterC59C2×#1442
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C25 ◁ C23×C4⋊C4

2942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 91257);