Finite Group Databasebeta

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C2×C4×#14579126 #34446464

order20224
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#14579126

Splittings

SylowC79 ⋊ C2×C42×Q8

Subgroups

subgroupG/H
centerC23×C4C22×D79
commutatorC2×C79C23×C42
FrattiniC23C24×D79
FittingC2×C4×C4⋊C4×C79C2
socle, prime radicalC24×C79C24
cosocleC23×C79C25
hypercenterC2×C4×C4⋊C4D79
hypocenterC79C2×C42×Q8
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

3966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20224

Conjugacy classes & character table

3280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 327763);