Finite Group Databasebeta

#20265618

order6464
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

FittingC2×Q16×C101 ⋊ C2
SylowC101 ⋊ #510

Subgroups

subgroupG/H
centerC2C2×#13108059
commutatorC8×C101C23
FrattiniC8C22×D101
FittingC2×Q16×C101C2
socleC2×C101C2×D8
hypercenterC2×Q16D101
hypocenterC101#510
LCSG ▷ C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,101|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^100,d^b=de,e^b=ef

Conjugacy classes & character table

716 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#27173021, #27173026, #27173081, …
maximal normal subgroup of#27173021, #27173026, #27173081, …
maximal quotient of#27172842, #27172852, #27172918, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6464, 990);