Finite Group Databasebeta

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C22×H(5,𝔽2)×D67 #31769716

order17152
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC22×H(5,𝔽2)×D67

Splittings

FittingC22×H(5,𝔽2)×C67 ⋊ C2
SylowC67 ⋊ C23×H(5,𝔽2)

Subgroups

subgroupG/H
centerC23C24×D67
commutator, cosocleC2×C67C27
FrattiniC2C26×D67
FittingC22×H(5,𝔽2)×C67C2
socleC23×C67C25
hypercenterC22×H(5,𝔽2)D67
hypocenterC67C23×H(5,𝔽2)
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

65726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1083453);