Finite Group Databasebeta

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C3×C5×C13×Dic15 #26043529

order11700
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×Dic15
unambiguous semidirect productC3⋊(C3×C5×C13×Dic5)

Splittings

derivedC3×C5 ⋊ C3×C4×C5×C13
HallC32×C52×C13 ⋊ C4
HallC52×C13 ⋊ C3×Dic3
HallC32×C52 ⋊ C4×C13
HallC32×C13 ⋊ C5×Dic5
SylowC52 ⋊ C3×Dic3×C13
SylowC32 ⋊ C5×C13×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C13D15
commutator, hypocenterC3×C5C3×C4×C5×C13
FrattiniC2C3×C5×C13×D15
Fitting, socle, prime radicalC2×C32×C52×C13C2
cosocleC2×C3×C5C2×C3×C5×C13
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C5×C13

160 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

3510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 376);