Finite Group Databasebeta

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C3×#15668515⋊C3 #39907995

order26100
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×#15668515⋊C3
unambiguous semidirect product#15668515⋊C32
unambiguous semidirect product(C3×#15668515)⋊C3

Splittings

derived, HallC52×C29 ⋊ C32×C4
HallC3×C29×C52⋊C3 ⋊ C4
Hall#15668515 ⋊ C32
HallC3×C52⋊C3 ⋊ Dic29
SylowC29 ⋊ C3×#1039⋊C3
SylowC52 ⋊ C32×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C3C29⋊((C5⋊D5)⋊C3)
commutator, hypocenterC52×C29C32×C4
FrattiniC2C3×C29⋊((C5⋊D5)⋊C3)
Fitting, socleC2×C3×C52×C29C2×C3
prime radicalC2×C3×C29×C52⋊C3C2
cosocleC2×C52×C29C2×C32
LCSG ▷ C52×C29
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5220

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 229);