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C2×C4×C4⋊(C79⋊C8) #34286140

order20224
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊(C79⋊C8)

Splittings

SylowC79 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC22×C42C2×D79
commutatorC2×C79C22×C4×C8
FrattiniC22×C4C23×D79
FittingC2×C43×C79C2
socle, prime radicalC24×C79C22×C4
cosocleC22×C4×C79C24
hypercenterC2×C43D79
hypocenterC79C2×C4×C4⋊C8
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C42 ◁ C2×C43

1550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20224

Conjugacy classes & character table

5152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 167439);