Finite Group Databasebeta

C2×#11777340 #72255356

order2304
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×#11777340

Splittings

SylowC32 ⋊ C2×#1580

Subgroups

subgroupG/H
centerC22×C4D4×C3⋊D3
commutatorC32×C4C23×C8
FrattiniC42C23×C3⋊D3
FittingC2×C32×C4×D8C2
socleC23×C32C4×D4
prime radicalC22×C32×D8C4
cosocleC32×C42C24
hypercenterC2×C4×D8C3⋊D3
hypocenterC32C2×#1580
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

2682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#72222464, C2×C3⋊D3×#1580, C2×#72222571
maximal normal subgroup ofC2×#72222464, C2×C3⋊D3×#1580, C2×#72222571
maximal quotient ofC2×#72222464

GAP

Past the SmallGroups library coverage — no SmallGroups id.