Finite Group Databasebeta

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C5×C11×AGL(1,𝔽5)×C23 #38760783

order25300
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×AGL(1,𝔽5)×C23

Splittings

Fitting, socle, HallC52×C11×C23 ⋊ C4
derivedC5 ⋊ C4×C5×C11×C23
HallC52×C23 ⋊ C4×C11
HallC52×C11 ⋊ C4×C23
SylowC52 ⋊ C4×C11×C23

Subgroups

subgroupG/H
center, hypercenterC5×C11×C23AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C11×C23
FrattiniC1G
Fitting, socleC52×C11×C23C4
prime radicalC5×D5×C11×C23C2
cosocleD5C2×C5×C11×C23
LCSG ▷ C5
UCSC1 ◁ C5×C11×C23

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5060

Conjugacy classes & character table

6325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 120);