Finite Group Databasebeta

C22×C4×#11758222 #30586587

order15616
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×#11758222

Splittings

FittingC23×C42×C61 ⋊ C2
SylowC61 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC22×C42C2×D61
commutatorC2×C61C25×C4
FrattiniC22C25×D61
FittingC23×C42×C61C2
socleC24×C61C24
prime radicalC23×#11758222C2
cosocleC22×C61C26
hypercenterC23×C42D61
hypocenterC61C22×C4×#41
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C42 ◁ C23×C42

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1076142);