Finite Group Databasebeta

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C3×C5×AGL(1,𝔽5)×C109 #45658307

order32700
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C109 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×AGL(1,𝔽5)×C109

Splittings

Fitting, socle, HallC3×C52×C109 ⋊ C4
derivedC5 ⋊ C3×C4×C5×C109
HallC52×C109 ⋊ C3×C4
HallC3×C52 ⋊ C4×C109
SylowC52 ⋊ C3×C4×C109

Subgroups

subgroupG/H
center, hypercenterC3×C5×C109AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C5×C109
FrattiniC1G
Fitting, socleC3×C52×C109C4
prime radicalC3×C5×D5×C109C2
cosocleD5C2×C3×C5×C109
LCSG ▷ C5
UCSC1 ◁ C3×C5×C109

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6540

Conjugacy classes & character table

8175 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 143);