Finite Group Databasebeta

C2×#21445789 #29679348

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21445789

Splittings

SylowC61 ⋊ C2×#1795

Subgroups

subgroupG/H
centerC22#16839618
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC22×H(5,𝔽2)×C61C2
socleC22×C61#379
cosocleC22×C4×C61C24
hypercenterC22×H(5,𝔽2)D61
hypocenterC61C2×#1795
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×H(5,𝔽2)

3946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

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, 168903);