Finite Group Databasebeta

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C4×C4⋊#10597845 #23758212

order10048
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊#10597845

Splittings

FittingC42×C157 ⋊ C4
SylowC157 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC2×C4C2×#10597845
commutatorC2×C157C2×C42
FrattiniC22C22×#10597845
FittingC42×C157C4
socleC22×C157C22×C4
prime radical, cosocleC22×D157C23
hypercenterC42#10597845
hypocenterC157C4×C4⋊C4
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42

194 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

664 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#34114970, #34114971, #34114986, …
maximal normal subgroup of#34114970, #34114971, #34114986, …
maximal quotient ofC4×(C2×#10597845)⋊C4, #34115312, #34115314, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1488);