Finite Group Databasebeta

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C3×C5×#14559102 #49137708

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11

Aliases

direct productC3×C5×#14559102

Splittings

Fitting, socle, HallC3×C52×C112 ⋊ C4
derivedC5×C112 ⋊ C3×C4×C5
HallC52×C112 ⋊ C3×C4
HallC3×C112 ⋊ C5×Dic5
SylowC112 ⋊ C3×C5×Dic5
HallC3×C52 ⋊ #92150
SylowC52 ⋊ C3×#92150

Subgroups

subgroupG/H
center, hypercenterC3×C5#14559102
commutator, hypocenterC5×C112C3×C4×C5
FrattiniC1G
Fitting, socleC3×C52×C112C4
prime radicalC3×C52×C11⋊D11C2
cosocleC5×C11⋊D11C2×C3×C5
LCSG ▷ C5×C112
UCSC1 ◁ C3×C5

256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

2370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 844);