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C4×H(5,𝔽2)×D17 #17940923

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×H(5,𝔽2)×D17

Splittings

FittingC4×C17×H(5,𝔽2) ⋊ C2
SylowC17 ⋊ C2×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C24×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC4×C17×H(5,𝔽2)C2
socle, cosocleC22×C17C26
prime radicalC2×H(5,𝔽2)×D17C2
hypercenterC4×H(5,𝔽2)D17
hypocenterC17C2×C4×H(5,𝔽2)
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

12378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076167);