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C3×C5×AGL(1,𝔽5)×C103 #44525503

order30900
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C103 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×AGL(1,𝔽5)×C103

Splittings

Fitting, socle, HallC3×C52×C103 ⋊ C4
derivedC5 ⋊ C3×C4×C5×C103
HallC52×C103 ⋊ C3×C4
HallC3×C52 ⋊ C4×C103
SylowC52 ⋊ C3×C4×C103

Subgroups

subgroupG/H
center, hypercenterC3×C5×C103AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C5×C103
FrattiniC1G
Fitting, socleC3×C52×C103C4
prime radicalC3×C5×D5×C103C2
cosocleD5C2×C3×C5×C103
LCSG ▷ C5
UCSC1 ◁ C3×C5×C103

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6180

Conjugacy classes & character table

7725 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30900, 109);