Finite Group Databasebeta

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C2×C4×C4⋊#1044 #72223140

order3200
isoclinismisoclinic class of #87863
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4×C5

Aliases

direct productC2×C4×C4⋊#1044

Splittings

FittingC2×C42×C52 ⋊ C4
SylowC52 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×#1044
commutatorC2×C52C22×C42
FrattiniC22C23×#1044
FittingC2×C42×C52C4
socleC23×C52C22×C4
prime radicalC23×C5⋊D5C23
cosocleC22×C5⋊D5C24
hypercenterC2×C42#1044
hypocenterC52C2×C4×C4⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C4 ◁ C2×C42

2354 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 ofC2×C4×#11717363
maximal normal subgroup ofC2×C4×#11717363
maximal quotient of#72223142

GAP

Past the SmallGroups library coverage — no SmallGroups id.