Finite Group Databasebeta

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C3×C112×Dic15 #36345035

order21780
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC3×C112×Dic15
unambiguous semidirect productC3⋊(C3×C112×Dic5)

Splittings

derivedC3×C5 ⋊ C3×C4×C112
HallC32×C5×C112 ⋊ C4
HallC32×C112 ⋊ Dic5
HallC5×C112 ⋊ C3×Dic3
HallC32×C5 ⋊ C4×C112
SylowC32 ⋊ C112×Dic5
SylowC5 ⋊ C3×C112×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C112D15
commutator, hypocenterC3×C5C3×C4×C112
FrattiniC2C3×C112×D15
Fitting, socle, prime radicalC2×C32×C5×C112C2
cosocleC2×C3×C5C2×C3×C112
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C112

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6534 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 384);