Finite Group Databasebeta

C2×#21460783 #30604438

order15616
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21460783

Splittings

SylowC61 ⋊ C2×#1336

Subgroups

subgroupG/H
centerC2×C4#14519839
commutatorC8×C61C22×C8
FrattiniC2×C8C22×#6923
Fitting, prime radicalC2×#135×C61C4
socleC22×C61D4⋊C8
cosocleC8×Dic61C23
hypercenterC2×#135#6923
hypocenterC61C2×#1336
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1093993);