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C4⋊C4×#1142 #13372195

order1792
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×#1142

Splittings

SylowC7 ⋊ C4⋊C4×SD16

Subgroups

subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×D4×C4⋊C4C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenterD4×C4⋊C4D7
hypocenterC7C4⋊C4×SD16
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

1030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 187967);