Finite Group Databasebeta

C22×#16840830 #30626726

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

Aliases

direct productC22×#16840830
unambiguous semidirect productD61⋊(C2×#519)

Splittings

FittingC23×Q8×C61 ⋊ C4
SylowC61 ⋊ C22×#519

Subgroups

subgroupG/H
centerC23C23×#6923
commutatorC2×C61C25×C4
FrattiniC2C25×#6923
FittingC23×Q8×C61C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC2×D61C26
hypercenterC23×Q8#6923
hypocenterC61C22×#519
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×Q8

11230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 1116281);