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C4⋊C4×#11929608 #34286263

order20224
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4⋊C4×#11929608

Splittings

SylowC79 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D79
commutatorC22×C79C22×C42
FittingC2×C4×C4⋊C4×C79C2
socleC23×C79C23×C4
prime radicalC24×C79C22×C4
cosocleC22×C4×C79C24
hypercenterC2×C4×C4⋊C4D79
hypocenterC79C4⋊C4×M16
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 167562);