Finite Group Databasebeta

C2×#21445927 #29679868

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21445927

Splittings

SylowC61 ⋊ C2×#1828

Subgroups

subgroupG/H
centerC22#16839625
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#518C2
socleC22×C61#381
prime radicalC23×D4×C61C22
cosocleC24×C61C24
hypercenterC2×#518D61
hypocenterC61C2×#1828
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C2×#518

1554 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, 169423);