Finite Group Databasebeta

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C5×C13×Dic117 #44477606

order30420
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic117
unambiguous semidirect productC9⋊(C5×C13×Dic13)

Splittings

derivedC9×C13 ⋊ C4×C5×C13
HallC5×C9×C132 ⋊ C4
HallC9×C132 ⋊ C4×C5
HallC5×C132 ⋊ Dic9
SylowC132 ⋊ C5×Dic9
HallC5×C9 ⋊ C13×Dic13
SylowC9 ⋊ C5×C13×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D117
commutator, hypocenterC9×C13C4×C5×C13
FrattiniC2×C3C5×C13×D39
FittingC2×C5×C9×C132C2
socle, prime radicalC2×C3×C5×C132D3
cosocleC2×C9×C13C2×C5×C13
LCSG ▷ C9×C13
UCSC1 ◁ C2×C5×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

7800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 195);