Finite Group Databasebeta

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C2×C4⋊C4×#1043 #72242360

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×#1043

Splittings

FittingC2×C52×C4⋊C4 ⋊ C4
SylowC52 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23C22×#1043
commutatorC2×C52C22×C42
FrattiniC22C23×#1043
FittingC2×C52×C4⋊C4C4
socleC23×C52C22×C4
prime radicalC23×C5⋊D5C23
cosocleC22×C5⋊D5C24
hypercenterC2×C4⋊C4#1043
hypocenterC52C2×C4×C4⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C4⋊C4

3712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#106×#1043, C2×#72220668, C2×C4×D4×#1043, …
maximal normal subgroup ofC2×#106×#1043, C2×#72220668, C2×C4×D4×#1043, …
maximal quotient ofC2×#106×#1043, C2×#72220668, C2×#108×#1043, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.