Finite Group Databasebeta

C22×#16839761 #30543545

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16839761

Splittings

FittingC23×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C22×#417

Subgroups

subgroupG/H
centerC24C2×C22⋊D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC23×C4⋊C4×C61C2
socleC24×C61C2×D4
prime radicalC23×#11758222C2
cosocleC2×C4×C61C25
hypercenterC23×C4⋊C4D61
hypocenterC61C22×#417
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C4⋊C4

5502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033100);