Finite Group Databasebeta

C22×#16839825 #30543842

order15616
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16839825

Splittings

FittingC22×C22⋊C8×C61 ⋊ C2
SylowC61 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC2×C61C24×C8
FrattiniC2×C4C24×D61
FittingC22×C22⋊C8×C61C2
socleC24×C61C22×C4
prime radicalC23×C22⋊D61C4
cosocleC2×C4×C61C25
hypercenterC22×C22⋊C8D61
hypocenterC61C22×C8×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033397);