Finite Group Databasebeta

C2×#11771325 #72245960

order2304
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×#11771325

Splittings

SylowC32 ⋊ C2×#1313

Subgroups

subgroupG/H
centerC22×C4C4×C3⋊Dic3
commutatorC32×C4C2×C4×C8
FrattiniC4×C8C22×C3⋊D3
FittingC2×C32×#346C2
socle, prime radicalC23×C32#97
cosocleC32×C4×C8C23
hypercenterC2×#346C3⋊D3
hypocenterC32C2×#1313
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×#346

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2304

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3⋊D3×#1313, C2×#72222571
maximal normal subgroup ofC2×C3⋊D3×#1313, C2×#72222571
maximal quotient ofC2×#72245441

GAP

Past the SmallGroups library coverage — no SmallGroups id.