Finite Group Databasebeta

C22×#16840829 #30626725

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

Aliases

direct productC22×#16840829
unambiguous semidirect productD61⋊(C2×#518)

Splittings

FittingC23×D4×C61 ⋊ C4
SylowC61 ⋊ C22×#518

Subgroups

subgroupG/H
centerC23C23×#6923
commutatorC2×C61C25×C4
FrattiniC2C25×#6923
FittingC23×D4×C61C4
socleC23×C61C23×C4
prime radicalC23×D4×D61C2
cosocleC2×D61C26
hypercenterC23×D4#6923
hypocenterC61C22×#518
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×D4

14590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1116280);