Finite Group Databasebeta

C2×#21455225 #30546752

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

Aliases

direct productC2×#21455225

Splittings

SylowC61 ⋊ C2×#3028

Subgroups

subgroupG/H
centerC22C2×#14519746
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
Fitting, prime radicalC2×C61×#585C2
socleC22×C61C2×#120
hypercenterC2×#585D61
hypocenterC61C2×#3028
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#585

4790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2098 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1036307);