Finite Group Databasebeta

C2×#21446052 #29680875

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

Aliases

direct productC2×#21446052

Splittings

SylowC61 ⋊ C2×#1860

Subgroups

subgroupG/H
centerC23#14519746
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#520C2
socleC23×C61#120
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#520D61
hypocenterC61C2×#1860
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#520

1478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 170430);