Finite Group Databasebeta

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C3×C5×C29×Dic15 #39908013

order26100
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C29×Dic15
unambiguous semidirect productC3⋊(C3×C5×Dic5×C29)

Splittings

derivedC3×C5 ⋊ C3×C4×C5×C29
HallC32×C52×C29 ⋊ C4
HallC52×C29 ⋊ C3×Dic3
HallC32×C29 ⋊ C5×Dic5
HallC32×C52 ⋊ C4×C29
SylowC52 ⋊ C3×Dic3×C29
SylowC32 ⋊ C5×Dic5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C29D15
commutator, hypocenterC3×C5C3×C4×C5×C29
FrattiniC2C3×C5×C29×D15
Fitting, socle, prime radicalC2×C32×C52×C29C2
cosocleC2×C3×C5C2×C3×C5×C29
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C5×C29

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 →

Presentation

transitive degreeμt(G) = 1740

Conjugacy classes & character table

7830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 247);