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C5×#17983787 #36345276

order21780
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3×C11

Aliases

direct productC5×#17983787

Splittings

Fitting, socle, HallC32×C5×C112 ⋊ C4
derived, HallC32×C112 ⋊ C4×C5
HallC5×C112 ⋊ #157
SylowC112 ⋊ C5×#157
HallC32×C5 ⋊ #92150
SylowC32 ⋊ C5×#92150

Subgroups

subgroupG/H
center, hypercenterC5#17983787
commutator, hypocenterC32×C112C4×C5
FrattiniC1G
Fitting, socleC32×C5×C112C4
prime radicalC5×C3⋊(C3⋊(C11⋊D11))C2
cosocleC3⋊(C3⋊(C11⋊D11))C2×C5
LCSG ▷ C32×C112
UCSC1 ◁ C5

184 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 625);