Finite Group Databasebeta

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C2×C23×D357 #45659338

order32844
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D357
unambiguous semidirect product(C2×C3)⋊(C23×D119)
unambiguous semidirect product(C2×C7)⋊(C23×D51)
unambiguous semidirect product(C2×C17)⋊(C23×D21)

Splittings

Fitting, socleC2×C3×C7×C17×C23 ⋊ C2
derived, HallC3×C7×C17 ⋊ C22×C23
HallC3×C7×C17×C23 ⋊ C22
HallC7×C17×C23 ⋊ C2×D3
HallC3×C17×C23 ⋊ C2×D7
HallC3×C7×C23 ⋊ C2×D17
HallC17×C23 ⋊ C2×D21
HallC7×C23 ⋊ C2×D51
HallC7×C17 ⋊ C2×D3×C23
HallC3×C23 ⋊ C2×D119
HallC3×C17 ⋊ C2×D7×C23
HallC3×C7 ⋊ C2×C23×D17
SylowC17 ⋊ C2×C23×D21
SylowC7 ⋊ C2×C23×D51
SylowC3 ⋊ C2×C23×D119

Subgroups

subgroupG/H
center, hypercenterC2×C23D357
commutator, cosocle, hypocenterC3×C7×C17C22×C23
FrattiniC1G
Fitting, socleC2×C3×C7×C17×C23C2
LCSG ▷ C3×C7×C17
UCSC1 ◁ C2×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16422

Conjugacy classes & character table

8280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 103);