Finite Group Databasebeta

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C3×C5×Dic285 #30685686

order17100
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic285
unambiguous semidirect productC3⋊(C3×C5×Dic95)

Splittings

derivedC3×C5×C19 ⋊ C3×C4×C5
HallC32×C52×C19 ⋊ C4
HallC52×C19 ⋊ C3×Dic3
HallC32×C52 ⋊ Dic19
HallC32×C19 ⋊ C5×Dic5
SylowC52 ⋊ C3×Dic57
SylowC19 ⋊ C3×C5×Dic15
SylowC32 ⋊ C5×Dic95

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D285
commutator, hypocenterC3×C5×C19C3×C4×C5
FrattiniC2C3×C5×D285
Fitting, socle, prime radicalC2×C32×C52×C19C2
cosocleC2×C3×C5×C19C2×C3×C5
LCSG ▷ C3×C5×C19
UCSC1 ◁ C2×C3×C5

160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 1140

Conjugacy classes & character table

4320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 323);