Finite Group Databasebeta

C2×#21455114 #30546447

order15616
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21455114

Splittings

SylowC61 ⋊ C2×#3011

Subgroups

subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
Fitting, prime radicalC22×2−1+4×C61C2
socleC23×C61C22×D4
hypercenterC22×2−1+4D61
hypocenterC61C2×#3011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×2−1+4

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1036002);