Finite Group Databasebeta

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C2×#10710647 #72270001

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#10710647

Splittings

SylowC3 ⋊ C2×#12687

Subgroups

subgroupG/H
centerC23C2×#834
commutatorC24×C3C23×C4
FrattiniC22×D4C23×D3
Fitting, prime radicalC23×C3×#120C2
socleC23×C3C2×#99
cosocleC22×C3×D4C24
hypercenterC23×#120D3
hypocenterC3C2×#12687
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C25 ◁ C24×D4 ◁ C23×#120

22592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72219821, C2×#72231563, C2×D3×#12687, …
maximal normal subgroup ofC2×#72219821, C2×#72231563, C2×D3×#12687, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.