Finite Group Databasebeta

C2×#21445923 #29679857

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

Aliases

direct productC2×#21445923

Splittings

SylowC61 ⋊ C2×#1827

Subgroups

subgroupG/H
centerC2×C4#14519736
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×#41×C61C2
socleC22×C61#381
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×C4×#41D61
hypocenterC61C2×#1827
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×#117 ◁ C2×C4×#41

1354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

2464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 169412);