Finite Group Databasebeta

C22×C4×#11758194 #30543401

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×C4×#11758194

Splittings

SylowC61 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC22×C42C2×D61
commutatorC2×C61C23×C42
FrattiniC2×C4C24×D61
FittingC23×C42×C61C2
socleC24×C61C22×C4
prime radicalC25×C61C2×C4
cosocleC2×C4×C61C25
hypercenterC23×C42D61
hypocenterC61C22×C4×M16
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C42 ◁ C23×C42

3950 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, 1032956);