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C5×AGL(1,𝔽5)×C361 #49115458

order36100
automorphism?
homologyAbelianization (H1) = C4×C5×C361 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽5)×C361

Splittings

Fitting, HallC52×C361 ⋊ C4
derivedC5 ⋊ C4×C5×C361
SylowC52 ⋊ C4×C361

Subgroups

subgroupG/H
center, hypercenterC5×C361AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C361
FrattiniC19C5×C19×AGL(1,𝔽5)
FittingC52×C361C4
socleC52×C19C4×C19
prime radicalC5×D5×C19C2×C19
cosocleD5×C19C2×C5×C19
LCSG ▷ C5
UCSC1 ◁ C5×C361

39 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7220

Conjugacy classes & character table

9025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36100, 19);