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C2×C4×Dic79⋊C8 #34286141

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

Aliases

direct productC2×C4×Dic79⋊C8

Splittings

SylowC79 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC22×C42C2×D79
commutatorC2×C79C22×C4×C8
FrattiniC22×C4C23×D79
FittingC22×C4×C8×C79C2
socle, prime radicalC24×C79C22×C4
cosocleC22×C4×C79C24
hypercenterC22×C4×C8D79
hypocenterC79C2×C4×C4⋊C8
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

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, 167440);