Finite Group Databasebeta

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C4×#11713200 #72244122

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#11713200

Splittings

FittingC4×#2846 ⋊ D3

Subgroups

subgroupG/H
centerC2×C4C2×#1020⋊C2
commutatorC2×C22⋊A4C23×C4
Frattini, socleC24C23×S4
FittingC4×#2846D3
prime radicalC2×#11713200C2
cosocleC22×C22⋊A4C24
hypercenterC22×C4#1020⋊C2
hypocenterC22⋊A4C2×C4×D4
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C2×C4 ◁ C22×C4

At least 8868 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#11713200, C4×#72209832, C4×#72215886, …
maximal normal subgroup ofC4×D4×#1020⋊C2
maximal quotient ofAGL(1,𝔽5)×#11713200, C4×#72215886, #72342093
automorphism group ofC2×C5×#41

GAP

Past the SmallGroups library coverage — no SmallGroups id.