Finite Group Databasebeta

C22×C4×#11745685 #29495263

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×#11745685

Splittings

FittingC23×C42×C59 ⋊ C2
SylowC59 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC22×C42C2×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
FittingC23×C42×C59C2
socleC24×C59C24
prime radicalC23×#11745685C2
cosocleC22×C59C26
hypercenterC23×C42D59
hypocenterC59C22×C4×#41
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C42 ◁ C23×C42

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076142);