Finite Group Databasebeta

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C52×C9×Dic13 #26043243

order11700
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C4×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC52×C9×Dic13

Splittings

derived, SylowC13 ⋊ C4×C52×C9
HallC52×C9×C13 ⋊ C4
HallC52×C13 ⋊ C4×C9
HallC9×C13 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52×C9D13
commutator, hypocenterC13C4×C52×C9
FrattiniC2×C3C3×C52×D13
FittingC2×C52×C9×C13C2
socle, prime radicalC2×C3×C52×C13C2×C3
cosocleC2×C3×C13C2×C3×C52
LCSG ▷ C13
UCSC1 ◁ C2×C52×C9

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 90);