Finite Group Databasebeta

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C2×#72221860 #72244175

order17496
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C23

Aliases

direct productC2×#72221860

Splittings

FittingC2×#14554150 ⋊ C22
derived#6903 ⋊ C23×C9
Sylow#14554150 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC2#72221860
commutator, hypocenter#6903C23×C9
FrattiniC3×C9C2×C3×#1113
FittingC2×#14554150C22
socleC2×C3#72221859
prime radicalC2×#72221848C3
cosocle#10624918C23×C3
LCSG ▷ #6903
UCSC1 ◁ C2

1500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#72221873

GAP

Past the SmallGroups library coverage — no SmallGroups id.