Finite Group Databasebeta

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C4×#11717438 #72221050

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11717438

Splittings

FittingC2×C42×C52 ⋊ C4
SylowC52 ⋊ C4×#117

Subgroups

subgroupG/H
centerC42C2×#1043
commutatorC2×C52C22×C42
FrattiniC22C23×#1043
FittingC2×C42×C52C4
socleC22×C52C23×C4
prime radicalC23×C5⋊D5C23
cosocleC22×C5⋊D5C24
hypercenterC2×C42#1043
hypocenterC52C4×#117
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C42 ◁ C2×C42

3008 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72221206, #72223250, C4×#41×#1043, …
maximal normal subgroup of#72221206, #72223250, C4×#41×#1043, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.